{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "google",
   "metadata": {},
   "source": [
    "##### Copyright 2023 Google LLC."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "apache",
   "metadata": {},
   "source": [
    "Licensed under the Apache License, Version 2.0 (the \"License\");\n",
    "you may not use this file except in compliance with the License.\n",
    "You may obtain a copy of the License at\n",
    "\n",
    "    http://www.apache.org/licenses/LICENSE-2.0\n",
    "\n",
    "Unless required by applicable law or agreed to in writing, software\n",
    "distributed under the License is distributed on an \"AS IS\" BASIS,\n",
    "WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
    "See the License for the specific language governing permissions and\n",
    "limitations under the License.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "basename",
   "metadata": {},
   "source": [
    "# earliness_tardiness_cost_sample_sat"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "link",
   "metadata": {},
   "source": [
    "<table align=\"left\">\n",
    "<td>\n",
    "<a href=\"https://colab.research.google.com/github/google/or-tools/blob/main/examples/notebook/sat/earliness_tardiness_cost_sample_sat.ipynb\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/colab_32px.png\"/>Run in Google Colab</a>\n",
    "</td>\n",
    "<td>\n",
    "<a href=\"https://github.com/google/or-tools/blob/main/ortools/sat/samples/earliness_tardiness_cost_sample_sat.py\"><img src=\"https://raw.githubusercontent.com/google/or-tools/main/tools/github_32px.png\"/>View source on GitHub</a>\n",
    "</td>\n",
    "</table>"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "doc",
   "metadata": {},
   "source": [
    "First, you must install [ortools](https://pypi.org/project/ortools/) package in this colab."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "install",
   "metadata": {},
   "outputs": [],
   "source": [
    "%pip install ortools"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "description",
   "metadata": {},
   "source": [
    "\n",
    "Encodes a convex piecewise linear function.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "code",
   "metadata": {},
   "outputs": [],
   "source": [
    "from ortools.sat.python import cp_model\n",
    "\n",
    "\n",
    "class VarArraySolutionPrinter(cp_model.CpSolverSolutionCallback):\n",
    "    \"\"\"Print intermediate solutions.\"\"\"\n",
    "\n",
    "    def __init__(self, variables):\n",
    "        cp_model.CpSolverSolutionCallback.__init__(self)\n",
    "        self.__variables = variables\n",
    "        self.__solution_count = 0\n",
    "\n",
    "    def on_solution_callback(self):\n",
    "        self.__solution_count += 1\n",
    "        for v in self.__variables:\n",
    "            print(f\"{v}={self.Value(v)}\", end=\" \")\n",
    "        print()\n",
    "\n",
    "    def solution_count(self):\n",
    "        return self.__solution_count\n",
    "\n",
    "\n",
    "def earliness_tardiness_cost_sample_sat():\n",
    "    \"\"\"Encode the piecewise linear expression.\"\"\"\n",
    "\n",
    "    earliness_date = 5  # ed.\n",
    "    earliness_cost = 8\n",
    "    lateness_date = 15  # ld.\n",
    "    lateness_cost = 12\n",
    "\n",
    "    # Model.\n",
    "    model = cp_model.CpModel()\n",
    "\n",
    "    # Declare our primary variable.\n",
    "    x = model.NewIntVar(0, 20, \"x\")\n",
    "\n",
    "    # Create the expression variable and implement the piecewise linear function.\n",
    "    #\n",
    "    #  \\        /\n",
    "    #   \\______/\n",
    "    #   ed    ld\n",
    "    #\n",
    "    large_constant = 1000\n",
    "    expr = model.NewIntVar(0, large_constant, \"expr\")\n",
    "\n",
    "    # First segment.\n",
    "    s1 = model.NewIntVar(-large_constant, large_constant, \"s1\")\n",
    "    model.Add(s1 == earliness_cost * (earliness_date - x))\n",
    "\n",
    "    # Second segment.\n",
    "    s2 = 0\n",
    "\n",
    "    # Third segment.\n",
    "    s3 = model.NewIntVar(-large_constant, large_constant, \"s3\")\n",
    "    model.Add(s3 == lateness_cost * (x - lateness_date))\n",
    "\n",
    "    # Link together expr and x through s1, s2, and s3.\n",
    "    model.AddMaxEquality(expr, [s1, s2, s3])\n",
    "\n",
    "    # Search for x values in increasing order.\n",
    "    model.AddDecisionStrategy([x], cp_model.CHOOSE_FIRST, cp_model.SELECT_MIN_VALUE)\n",
    "\n",
    "    # Create a solver and solve with a fixed search.\n",
    "    solver = cp_model.CpSolver()\n",
    "\n",
    "    # Force the solver to follow the decision strategy exactly.\n",
    "    solver.parameters.search_branching = cp_model.FIXED_SEARCH\n",
    "    # Enumerate all solutions.\n",
    "    solver.parameters.enumerate_all_solutions = True\n",
    "\n",
    "    # Search and print out all solutions.\n",
    "    solution_printer = VarArraySolutionPrinter([x, expr])\n",
    "    solver.Solve(model, solution_printer)\n",
    "\n",
    "\n",
    "earliness_tardiness_cost_sample_sat()\n",
    "\n"
   ]
  }
 ],
 "metadata": {},
 "nbformat": 4,
 "nbformat_minor": 5
}
